that face jesus

Did Jesus's manger ever become an artifact of interest like the Grail or the Lance?

Not that I am aware of. A church in Croatia claims to have his swaddling clothes, though.

The main relics of Jesus are bits of the True Cross, the Shroud of Turin, the Sudarium of Ovieda (a cloth wrapped around Jesus’s head after his death), the Mandylion, the Veil of Veronica (these are both cloths with Jesus’s face on them like the Shroud of Turin), the Holy Grail, the Crown of Thorns, vials of his blood, a crown made from the crucifixion nails, a bridle ALSO made from these nails, the Holy Lance aka the Spear of Destiny, the Holy Sponge, the column Jesus was tied to when they whipped him, the Gifts of the Magi, the knife used at the Last Supper, and, of course, the Holy Prepuce aka Jesus’s foreskin.